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Noncommutative Geometry and Particle Physics

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Noncommutative Geometry and Particle Physics/ by Walter D. van Suijlekom.
作者:	van Suijlekom, Walter D.
面頁冊數:	XVI, 237 p. 28 illus., 2 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Physics. -
電子資源:	https://doi.org/10.1007/978-94-017-9162-5
ISBN:	9789401791625

Noncommutative Geometry and Particle Physics
van Suijlekom, Walter D.

Noncommutative Geometry and Particle Physics[electronic resource] /by Walter D. van Suijlekom. - 1st ed. 2015. - XVI, 237 p. 28 illus., 2 illus. in color.online resource. - Mathematical Physics Studies,0921-3767. - Mathematical Physics Studies,.

Preface -- Introduction -- Part 1. Noncommutative geometric spaces -- Finite noncommutative spaces -- Finite real noncommutative spaces -- Noncommutative Riemannian spin manifolds -- The local index formula in noncommutative geometry -- Part 2. Noncommutative geometry and gauge theories -- Gauge theories from noncommutative manifolds -- Spectral invariants -- Almost-commutative manifolds and gauge theories -- The noncommutative geometry of electrodynamics -- The noncommutative geometry of Yang-Mills fields -- The noncommutative geometry of the Standard Model -- Phenomenology of the noncommutative Standard Model -- Bibliography.

This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model. .

ISBN: 9789401791625

Standard No.: 10.1007/978-94-017-9162-5doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Noncommutative Geometry and Particle Physics
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520 $a This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model. .
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